↑

Properties

Label 283746.t
Number of curves $2$
Conductor $283746$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 283746.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283746.t1 283746t1 \([1, 0, 1, -25639, 1570154]\) \(39616946929/226368\) \(10649681990208\) \([2]\) \(1990656\) \(1.3412\) \(\Gamma_0(N)\)-optimal
283746.t2 283746t2 \([1, 0, 1, -11199, 3331834]\) \(-3301293169/100082952\) \(-4708490649920712\) \([2]\) \(3981312\) \(1.6878\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283746.t have rank \(1\).

Complex multiplication

The elliptic curves in class 283746.t do not have complex multiplication.

Modular form 283746.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 4 q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} - 4 q^{10} + q^{12} - 6 q^{13} + 4 q^{14} + 4 q^{15} + q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.